Estimation of the Regression Equation Parameters X-Ray Radiometric and Geological Testing on Deposits of Rare and Precious Metals

Abstract

Abstract Analysers for x-ray radiometric testing (X-RRT) are graded by comparing the results with traditional geological testing (GT). This time-consuming operation involves the collection of several hundred tests and their subsequent analysis in the laboratory. The “selection” of the regression equation coefficients between the X-RRT and GT data is complicated by a large range of metal contents and extremely uneven its distribution in the ore zones. For these reasons, the standard deviations between the testing methods are large and vary widely depending on the metal content. To increase the accuracy of regression parameter estimates, it is necessary to enlarge the control sampling. Such method raises the cost of testing and reduces its efficiency at variability of textural and structural features of ores. 270 slime tests of drilling and blasting wells of silver deposit Dukat are used for the analysis. The silver content in the tests according to the assay analysis was from 20 to 10 000 and more g/t. The differences between the main and repeated GT in the intervals of silver content 50 – 239, 240 – 999, 1000 g/t and more were 76, 175 and 651 g/t, respectively. Estimates of the regression equation between the two methods of testing with the help of two algorithms are compared. In the first, the loss function determined by the sum squares residuals (values deviations of the dependent variable from the regression line), in the second – the sum of the absolute values of the residuals normalized by the sum of the values of the dependent and independent variables. As a result, it is shown that in the first case, in order to improve the accuracy of coefficient estimates, it is necessary to exclude observations in which the absolute value of the residuals normalized by their standard deviation exceeds the critical level of 5-7. The second method is resistant to sampling and the number of observations can be reduced by 2 -3 times. Under these conditions, the error of coefficient estimates is close.